Find the volume and the surface area of the solid.
8in 9in 6in
To find the volume of a solid, you need to multiply its length (L), width (W), and height (H), using the formula V = L x W x H.
Given that the length (L) is 8in, the width (W) is 9in, and the height (H) is 6in, the volume (V) can be calculated as follows:
V = 8in x 9in x 6in
V = 432in³
Therefore, the volume of the solid is 432 cubic inches.
To find the surface area of a solid, you need to calculate the area of each face and then add those areas together.
The solid has 6 faces: a top face, a bottom face, a front face, a back face, a left face, and a right face.
The top face and bottom face have the same dimensions and shape, so their areas are the same. The front face, back face, left face, and right face also have the same dimensions and shape, so their areas are equal as well.
To find the area of each of these faces, you need to multiply the length (L) by the width (W) for the top and bottom faces, and the length (L) by the height (H) for the front, back, left, and right faces.
Let's calculate the surface area (A) of the solid:
A = 2(L x W) + 2(L x H) + 2(W x H)
A = 2(8in x 9in) + 2(8in x 6in) + 2(9in x 6in)
A = 2(72in²) + 2(48in²) + 2(54in²)
A = 144in² + 96in² + 108in²
A = 348in²
Therefore, the surface area of the solid is 348 square inches.